Multiple choice

3 men and 18 women together take 2 days to complete a piece of work. How many days will 9 women alone take to complete the piece of work, if 6 men alone can complete the piece of work in 3 days?

  1. 5

  2. 6

  3. 7

  4. 9
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

3m + 18w = 1/2 work/day. 6m = 1/3 work/day, so 1m = 1/18 work/day. Substitute m: 3(1/18) + 18w = 1/2. 1/6 + 18w = 1/2. 18w = 1/3. w = 1/54. 9w = 9/54 = 1/6 work/day. Time = 6 days.

AI explanation

Using the total work method, 6 men finishing in 3 days means 1 man does 1/18 of the work per day. The equation for the first team is 3 men and 18 women equal 1/2 of the work per day, which means 3/18 plus 18 women equals 1/2. Solving this gives 1 woman equals 1/36 of the work per day. Therefore, 9 women will complete 9/36 of the work per day, finishing the job in 36/9 days. The answer is 6.

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